A 90-yard punt ; Quadratics

So upon my call last week for quadratic activities, I got a ton of resources in my inbox. I’ll post them soon after I’ve had a chance to look through them. Until then, here’s something I cooked up that could go several different directions, depending on your students’ needs.


This terribly grainy video of a famous “90 yard” punt (well, as famous as a punt could be) by NY Giants punter Rodney Williams. Get out your stopwatches.


Guiding Questions

  • How far did the punt travel?
  • How fast did the punt travel?
  • How high did the punt get?
  • Does the fact that the punt was in “Mile High” stadium in Denver have anything to do with this?

Suggested activities

  • Students sketch their basic anticipated path of the football. Something like this.

“Say that looks a lot like a parabola! Great job, students. You drew a parabola! What? You don’t know what a parabola is? Well, you just drew one….”

  • I hope the students had their stopwatch out. If not, they may have to see it again.

Or, for those without a stop-watch…

(side note: if you can find a better, less grainy video that would be fantastic. Sometimes they even put the hang-time right there on the screen in tenths of the second. That’s awesome.)

Looks like it had a hang time of 5 seconds. So, let’s try to answer some of the above questions.


Even though the punt takes place way up in Denver, I’m going to assume that gravity is pretty much the same at sea level. So the acceleration due to gravity is -9.8 m/s2.

So in the vertical it takes 5 second to go from the punter’s foot (which we’ll assume is a lot like the ground) to the ground at the ~16 yard line.

So the ball’s initial velocity in the vertical direction was about 24.5 m/s. If we move things around a bit, we can find the top of the ball’s trajectory (i.e. the height it reached). At the height of the ball’s trajectory t=2.5, so we have the following:

So at the height of the ball’s path, it made it to almost 31 meters. Let’s do a quick diagram-recap.

Another thing we could do to this is use Geogebra to recreate the punt, here. (note: this worksheet represents the first minute-and-a-half I used Geogebra. It could be a lot better.)

Can someone help me with my 5-year-old daughter’s Math homework? (Part 2)

So remember the first part of my quandary about my kid’s math homework from this morning? Well, now I’m on the next question and I’m stuck again.

I’m not sure what “do we see” means. Does it mean how many hats of the 17 do they both see? That could mean this.

Then again, “hats we see” could mean that she and I are in separate rooms and the questioner (me?) would like to know how many total hats do we see?

But then, there could be overlap of the “hats we see.” I could see 5 of the same hats my mom sees. In such an instance we would have this.

So I would suggest the answer to this question is “any integer from 0 to 17.”

Seems a bit in depth for Kindergarten if you ask me.

Brainstorming Quadratics

I’d like to do for Quadratics what we did with Pythagorean’s Theorem. I put out the call on Pythagorean’s Theorem and had come up with several ideas, only a couple of which were by me.

So I’m putting up the bat signal again. Except in this case it’s the quadratic formula signal and asking for your help. Please comment, email, or tweet me ideas, resources, youtube videos, or stuff you’ve done.

So far here’s some stuff I thought up.

  • Cars crashing – use quadratics and the acceleration formula to determine who’s at fault.

  • Remote control cars accelerating and decelerating. Plot and find the acceleration and deceleration of the cars. (should be a quadratic)
  • NFL punts. Find a nice video of an NFL punt with good hangtime and do some stuff with it.
  • Related: let’s get a punter to nail the giant TV in the new Cowboys stadium.

Until then, here’s a post by Dan Meyer on quadratics that is way, way more interesting than anything I’ll do (here’s the how-to).

Can someone help me with my 5-year-old daughter’s Math homework?

I’m being serious. It’s due tomorrow and I have no idea how to answer the following question.

Now, the answer to this is obviously “four.” The narrator has four cats. The number of cats his or her friend has is irrelevant to the question.

I’m just not sure how to fill in the pictures and symbols. Here’s what I have so far.

But I’m not sure what to put in between. So here’s my final answer. Please check my work.

Please give your students this quiz, and how big is a “bushel” anyway?

(h/t: Freakonomics blog)

The following is an actual test given to 8th grade students in Kansas in 1895, unearthed by the Salina Journal. Please refer to the “arithmetic” section.

Here are the “arithmetic” questions and my attempted responses:

1. Name and define the Fundamental Rules of Arithmetic.

Umm….. Please Excuse My Dear Aunt Sally?

2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold?

/1985 8th grader pushes wooden desk aside and grabs a laptop equipped with Google Sketch-up

Wait, how big is a bushel?

/1895 8th grader googles “how big is a bushel of hay”

/is unsuccessful

3. If a load of wheat weighs 3,942 pounds, what is it worth at 50 cts. per bu., deducting 1050 lbs. for tare?

Let’s see. I know that “tare” is something they do at the deli counter so you don’t end up paying for the slight weight of the bag holding your meat. So, I’m going to say I’m paying for 3942 lbs – 1050 lbs = 2892 lbs.

Now, 2892 lbs at 50 cts/bu….. ? “Bu?” Does that have anything to do with a bushel? Cause I’m out.

4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals?

What a coincidence! We still fund schools at the same rate of $50 a month NOW!

So let’s see, District No. 33 (not related to District 9) needs 7 x $50 = $350 and then $104 for “incidentals.” So they need a total of $454. So we need a levy against the $35000. Well, 454/35000 = 0.01297…

So there would need to be a levy of 1.3%. Good luck getting that tax bill passed in this political climate.

5. Find cost of 6,720 lbs. coal at $6.00 per ton.

Finally! An easy one! 6720 lbs = 3.36 tons (I thought it was spelled “tonnes” back then).

So that’s $20.16 for 3.36 tons at $6 per ton.

6. Find the interest of $512.60 for 8 months and 18 days at 7 per cent.

At 7% what, exactly? You see, they do these “early paycheck” scams nowadays where you pay like 7% interest per week or something.

7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20 per in.?

This is a trick question. You can’t pay for in “in.” as the question suggests. You pay according to “square inch”! Boomroasted!

8. Find bank discount on $300 for 90 days (no grace) at 10 per cent.

Um… 10% of $300 is $30…. Pass.

9. What is the cost of a square farm at $15 per acre, the distance around which is 640 rods?

Love this question. Every Geometry teacher on earth has asked a less-19th Century version of this question.

According to ye olde wikipedia, a “rod” is equal to 5.5 yards. So the fact that it’s a square and has a perimeter of 640 rods suggests the dimensions are 160 rods x 160 rods. Or 25600 square rods. Or 2640 ft. x 2640 ft = 6969600 sq. ft. An acre is 43560 sq. ft. So this farm has an acrage of 6969600/43560 = 160 acres.

At $15 an acre, that’s $2400.

They had calculators back then, right?

10. Write a Bank Check, a Promissory Note, and a Receipt.

Ummm.. Pass.

I absolutely love this last question though. Talk about authentic learning! I’m sure they had to be able to do this soon after they graduated the 8th grade. And I love that this is categorized under “arithmetic” and not “economics” or something.

I also love how the quiz is clearly Kansas-centric. It was just expected that students should know all about bushels, farms, and promissory notes. Localizing your assessment and activities can do wonders for comprehension.

The Wacky Algebra of NFL Passer Rating


The following formula calculates NFL Passer rating. (wiki)

(note: each component has a predetermined MAX and MIN value that appeared to be pulled out of thin air.)

Personally, I would simply present this equation to students at the beginning of class and let them stare at it a while and try to figure some things out in their heads. Eventually, the teacher and students should probably come up with some guiding questions.

Guiding Questions

  • Who came up with this thing?
  • Which “component” is most important to QB rating? Why?
  • Why aren’t rushing yards included? Could we include them? How?
  • Why do you divide by 6?
  • Why do you multiply by 100 at the end?
  • Does this convoluted formula correlate at all with being a good QB?
  • Does the formula change with era? Should it?
  • Can we change this formula to make Quarterback X look better? (There’s either a fan question or an agent question. For this region of the country, it would be John Elway.)

Suggested activities

There are a lot of routes you could go with it – comparing passer rating in different eras, creating your own formula that is either less or more complex, regressing passer rating with team offensive production to measure the importance of the quarterback and/or the validity of the formula – but I’m going to go one particular route: comparing the top two current career leaders in passer rating, who, as luck would have it, are still playing today.

Currently, the QB with the highest passer rating in NFL history (minimum 1500 attempts) is Green Bay quarterback (and apparently a regular personality here) Aaron Rodgers at 98.4 (stats can be found here). Phillip Rivers is second with 97.2 (stats found here). How many incompletion in a row would Rodgers have to throw in order to fall behind Rivers? How many interceptions would he have to throw in a row? Conversely, how many, say, touchdowns would Rivers have to throw to surpass Rodgers? Can we graph this mess?

The Pizza Casbah 30-inch pizza challenge

This is a picture of a single slice of pizza from my favorite pizza place in Fort Collins, Pizza Casbah.

My god that looks amazing. I’m getting hungry just looking at it.

This is a picture of an entire Pizza Casbah, 18-inch pizza (presumably, that means the diameter of the pizza is 18 inches):

It seriously is amazing pizza. And I can eat a lot of it.

A couple weeks ago, a friend and I were ordering a pizza from the online Pizza Casbah menu and we saw this (click to enlarge):

Now, I don’t mean to brag too much, but I really think I can eat anyone under the table when it comes to Pizza Casbah. I’ve never really gone head-to-head, or truly pushed my limits, but I’m fairly confident I can eat an entire 18-inch, 5-topping pizza by myself.

I really want my picture up on their wall-of-fame. I also really want a gift card for more Pizza Casbah.